Right now there are a lot of schools in the process of making a game design degree. There are not many right now, and they are extremly hard to get into. One for instance that I know off the top of my head is WPI. Which is a very good school and is pretty difficult to get into. They call this major: Interactive Media and Game Development.
However you will be seeing a lot more 4 year programs pop up everywhere as the gaming industry is now outperforming the movie industry based on gross money earned. So its a great field to get into, and now they can specialize people for games which is a good thing. Before you would just get a masters in computer science and then get into the game industry. A lot of the old game designers actually had PhD's also.